PRP Records

Probable Primes Top 10000

(212140 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
9001(74*10^54583+61)/954584Robert Price10/2015
90022^181316-9439554582Lelio R Paula09/2011
900314751^5006+5006^1475154572Hans Havermann08/2016
900414^47609+3954567Lelio R Paula02/2013
900512696^13295-13295^1269654559Norbert Schneider01/2018
9006(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
90083^114327-7454548Lelio R Paula10/2012
9007(44*10^54547-161)/954548Robert Price11/2017
9009gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
9010(17*10^54537-47)/354538Robert Price05/2017
90112^181155-1155*18115554534Henri Lifchitz02/2005
9012Phi(61672,83)54533Enzo Doria05/2012
9013(2*10^54527-197)/354527Robert Price11/2017
90149*2^181128+754526Lelio R Paula03/2014
901589*10^54518-754520Robert Price03/2017
90162^181090-11324754514Enzo Doria07/2014
901714031^7670+7670^1403154508Hans Havermann08/2016
901814210^6849+6849^1421054505Hans Havermann08/2016
90192^181043-19954500Lelio R Paula02/2011
902012^50499+554498Lelio R Paula01/2013
902112^50491+554489Lelio R Paula01/2013
90226^70016-14554484Lelio R Paula10/2012
902311^52313-960054479Enzo Doria02/2013
90242^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
90252^180946-11104154471Enzo Doria05/2014
9026(64*10^54467+287)/954468Robert Price04/2016
9027(32*10^54458+319)/954459Robert Price10/2017
90285^77907-2*3^7790754455Mike Oakes11/2009
902920^41853-562354453Enzo Doria03/2013
903014^47506-7554448Lelio R Paula02/2013
9031(25*10^54443-67)/354444Robert Price11/2017
90322^180839-11343754438Enzo Doria08/2014
90333^114085+2854433Lelio R Paula10/2012
9034Phi(141230,10)54432Ray Chandler08/2009
90356^69946-5554429Lelio R Paula10/2012
9036p(11796)#/2-102454427Robert Price09/2017
90375*2^180796+354426Lelio R Paula03/2014
9038(23*2^180782-1)/9154421Lelio R Paula01/2014
90399*6^69928-754416Lelio R Paula09/2014
904092^27701-91^2770154399Robert Price08/2015
9041(2^180687-3)*6-754393Gilbert Mozzo04/2016
9042(5*10^54388-11)/354389Erik Branger12/2013
904320^41799-304354382Enzo Doria03/2013
904413860^8387+8387^1386054382Hans Havermann08/2016
9045(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
90467^64329-1854365Lelio R Paula10/2012
90472^180551-96754352Yves Minet01/2012
904815^46209-7454347Lelio R Paula02/2013
904910^54345+2973954346Patrick De Geest08/2013
905010^54345-14138154345Patrick De Geest09/2013
9051lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
9052177^24171-254336Lelio R Paula10/2017
90532^180496+1554335Lelio R Paula02/2011
90541845^16636+16636^184554334Serge Batalov05/2014
905511^52169-7054329Lelio R Paula01/2013
90562^180446-403154320Yves Minet02/2018
905713693^9262+9262^1369354317Hans Havermann06/2016
90582^180429-11310154315Enzo Doria07/2014
90592^180423-11205154313Enzo Doria05/2014
906016112^2349+2349^1611254312Hans Havermann06/2016
9061(79^28621-1)/7854311Paul Bourdelais08/2017
9062(13^48751+4^48751)/1754305Robert Price05/2013
90632^180370+1291554297Lelio R Paula09/2012
9064(10^54290+41)/354290Robert Price01/2017
906515108^3917+3917^1510854283Hans Havermann06/2016
90662^180317-301954281Yves Minet10/2014
90672^180314+85554280Lelio R Paula10/2009
906819^42425+9454252Lelio R Paula02/2013
90692^180180-100544954240Paul Bourdelais11/2012
90702^180173-277354238Yves Minet07/2014
907113367^11418+11418^1336754238Hans Havermann06/2016
9072427^20614+20614^42754224Norbert Schneider06/2016
90732^180124-8795954223Gary Barnes08/2009
90742^180111-11310154219Enzo Doria07/2014
90752^180101-11487154216Enzo Doria05/2015
9076(11*2^180099+1)/5161754212Lelio R Paula07/2012
90772^180070+46554207Lelio R Paula09/2012
907813683^9154+9154^1368354207Hans Havermann06/2016
9079810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
90802^180014+61354190Jason Earls04/2008
90812^180007+10154188Lelio R Paula02/2011
90822^180001+4187754186Jim Fougeron08/2002
90832^180000+13015354186Jim Fougeron09/2002
90843^113565-7454185Lelio R Paula10/2012
908550^31891-4954182Norbert Schneider07/2014
9086(5*2^179991-1)/1142754180Lelio R Paula01/2014
90873^113548+2654177Lelio R Paula10/2012
9088(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
9089181^23996-254176Lelio R Paula10/2017
90904159^14969-13854173Enzo Doria07/2012
90912^179955+577554172Lelio R Paula10/2009
90922^179953-23131354172Enzo Doria05/2014
90935^77485+654160Lelio R Paula10/2012
909418^43141+8554154Lelio R Paula02/2013
909510^54149+18764754150Patrick De Geest07/2017
90983^113489-34054149Lelio R Paula10/2012
909610^54149-80000154149Robert Price06/2017
909710^54149-3650154149Patrick De Geest07/2017
90997^64070+9054146Lelio R Paula10/2012
910012549^13210-13210^1254954143Norbert Schneider12/2017
910118^43131+7154142Lelio R Paula02/2013
91022^179826-13154134Lelio R Paula02/2011
91032^179815-11273554130Enzo Doria06/2014
91042^179806+7384954127Enzo Doria04/2016
91052^179790+3354123Donovan Johnson02/2006
910614287^6138+6138^1428754120Hans Havermann06/2016
9107(17*10^54117+1)/954118Serge Batalov05/2010
91082^179763-18954115Lelio R Paula02/2011
9109(21181*2^179770+1)/302910554115Lelio R Paula05/2014
91101828^16589+16589^182854113Serge Batalov05/2014
911220^41588-588354108Enzo Doria03/2013
911150^31847-4954108Norbert Schneider07/2014
91132^179733-685554106Lelio R Paula10/2009
911420^41584-558354103Enzo Doria03/2013
911510^54084+3*3^5408454085Mike Oakes05/2010
91162^179613-179554069Lelio R Paula10/2009
91172^179589-101152354062Paul Bourdelais11/2012
91182^179574-253154058Yves Minet07/2014
9119(41*10^54051-23)/954052Robert Price05/2015
9120117^26131-11654044Norbert Schneider10/2013
9121(10^54038-31)/354038Serge Batalov12/2014
912211^51885-8454033Lelio R Paula01/2013
912314990^4011+4011^1499054013Hans Havermann07/2016
9124(19*2^179414+1)/754010Lelio R Paula07/2012
91253^113182-1040854002Enzo Doria02/2013
912635^34970-878653997Enzo Doria03/2013
91272^179371-163758753997Enzo Doria05/2015
912819^42225-9253996Lelio R Paula01/2013
912910190^13471-13471^1019053995Norbert Schneider05/2018
9130(3^113188+7)/7391767578453994Lelio R Paula03/2012
91317*3^113162+853993Lelio R Paula03/2014
9132(10^53991+179)/953991Serge Batalov12/2014
91332^179350-214553990Lelio R Paula10/2009
9134(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
91358^59782-6^59782-3^5978253989Mike Oakes11/2009
91363*7^63861+853970Lelio R Paula09/2014
91372^179274+7138953967Enzo Doria04/2016
91382^179259-5869553963Lelio R Paula10/2009
91396^69345+6153961Lelio R Paula10/2012
9140(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
9141(40216^11719-1)/4021553955Serge Batalov04/2015
914289*10^53951-953953Robert Price05/2017
914314^47067-353945Lelio R Paula01/2013
9144p(11700)#/2-51253937Robert Price07/2017
9145(2^179168-5)/5953934Lelio R Paula02/2012
91462^179128+841553923Lelio R Paula07/2012
91472^179120+253353921Henri Lifchitz09/2004
9149(2^179126+78557)/464932118753913Lelio R Paula05/2012
914874^28842+7353913Norbert Schneider11/2012
91501271^17368+17368^127153913Serge Batalov05/2014
91512^179079+5353909Lelio R Paula02/2011
915217^43807+5453903Lelio R Paula01/2013
915317^43807+3053903Lelio R Paula01/2013
91543^112951-31053892Lelio R Paula10/2012
9155Phi(7,2957!)53888Robert Price05/2015
9156(10223*2^178975+1)/3398553877Lelio R Paula05/2014
91572^178944-21920953868Enzo Doria11/2012
9158(10^53859+149)/353859Serge Batalov12/2014
91592^178910-19153858Lelio R Paula02/2011
916016170^2141+2141^1617053857Hans Havermann07/2016
9161(5*10^53855-107)/353856Robert Price01/2017
9162(72*10^53847-27)/9953847Patrick De Geest08/2004
91632^178841-86968810553837Lelio R Paula06/2012
91642*10^53834-2753835Robert Price02/2017
91662^178821-101152353831Paul Bourdelais11/2012
916512601^13128-13128^1260153831Norbert Schneider10/2017
91672^178819-1553830Lelio R Paula02/2011
9168(14450!-1)/22529658153829Donovan Johnson04/2006
9169(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
917010530^13381-13381^1053053825Norbert Schneider03/2018
91712^178761-46553813Lelio R Paula10/2009
917218900^703+703^1890053808Anatoly F. Selevich02/2007
917313918^7343+7343^1391853806Hans Havermann08/2016
917410^53804+3174953805Patrick De Geest12/2012
917510^53804-7153804Robert Price05/2011
9176t(178994)53804Robert Price03/2015
9177(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
91782^178671-11321553786Enzo Doria07/2014
917915110^3621+3621^1511053774Hans Havermann07/2016
91802^178611+9553768Lelio R Paula02/2011
91812^178597+571153764Lelio R Paula10/2011
91822^178598+1291553764Lelio R Paula07/2012
9183(9179*2^178579-1)/30353760Lelio R Paula03/2015
918410671^13342-13342^1067153745Norbert Schneider02/2018
91855*7^63589+253740Lelio R Paula09/2014
91862^178516-11251553739Enzo Doria06/2014
918720^41302-2753736Lelio R Paula01/2013
91886^69054-3920953735Mike Oakes12/2010
918913086^12769+12769^1308653734Hans Havermann07/2016
91902^178455+7604353721Enzo Doria04/2016
9191(10^53718-7)/353718Makoto Kamada10/2004
9192(67607*2^178426+1)/353716Lelio R Paula05/2014
91939*10^53707+1153708Robert Kinser01/2017
919494601!8-253708Robert Price04/2017
919513214^11595+11595^1321453706Hans Havermann07/2016
9196Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
91972^178367-37953694Yves Minet03/2013
9198(2^178364-5)/1153692Lelio R Paula02/2012
91994339^14760-16853688Enzo Doria06/2012
920012^49746-1153685Lelio R Paula01/2013
920112950^13051-13051^1295053670Norbert Schneider08/2017
9203(9913*2^178266-1)/224753665Lelio R Paula03/2015
920213725^8128+8128^1372553665Hans Havermann07/2016
92042^178250-11326153659Enzo Doria07/2014
92052^178226+1171553652Lelio R Paula10/2009
920635^34742-197653645Enzo Doria03/2013
920720^41228-56353639Enzo Doria03/2013
9208359^20992+20992^35953637Norbert Schneider08/2014
9209(27*2^178183-1)/2906553636Lelio R Paula01/2014
9210(3^112414+7)/3738169653628Lelio R Paula03/2012
921117994^955+955^1799453623Anatoly F. Selevich10/2006
92122^178117-155153619Yves Minet08/2012
92132^178099-1128753614Enzo Doria06/2014
921410751^13298-13298^1075153611Norbert Schneider01/2018
9215(15*2^178080-1)/30907153604Lelio R Paula01/2014
92165^76672-1376653592Enzo Doria02/2013
92176^68868-13753590Lelio R Paula10/2012
9218(5*2^178021+1)/817353587Lelio R Paula07/2012
92195^76654-2653579Lelio R Paula10/2012
9220(3^112297-2)/762753576Lelio R Paula03/2012
92213*2^177948-753569Lelio R Paula03/2014
922210^53558+1854353559Patrick De Geest12/2012
922310^53558-2153558Robert Price03/2011
92242^177792-9553521Lelio R Paula02/2011
922513392^9919+9919^1339253521Hans Havermann07/2016
922613105^12132+12132^1310553520Hans Havermann07/2016
922713^48042+8253517Lelio R Paula01/2013
92282^177768+3912153514Yves Minet10/2010
922913835^7366+7366^1383553504Hans Havermann07/2016
923017^43477+8453497Lelio R Paula01/2013
92315*10^53492+953493Dmitry Domanov11/2010
92322^177683+9553488Lelio R Paula01/2011
923311057^13226-13226^1105753482Norbert Schneider12/2017
9234(2^177678+3)/51462753481Lelio R Paula02/2012
92352^177641-25546353476Gary Barnes08/2009
9236p(11608)#/2+1653469Robert Price12/2016
9237(14*10^53465+211)/953466Robert Price11/2017
923837302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
923912001^13104-13104^1200153455Norbert Schneider10/2017
92401829^16384+1828^1638453449Henri Lifchitz01/2007
924110^53442+1262153443Patrick De Geest06/2018
924210^53442-200753442Patrick De Geest06/2018
924335^34608-960253438Enzo Doria03/2013
9244(3^111992+8)/1486753430Lelio R Paula03/2012
92462^177480+186966153427Enzo Doria05/2016
924511791^13122-13122^1179153427Norbert Schneider10/2017
9247(8*10^53411+1)/953411Serge Batalov12/2008
92484*5^76410-353409Lelio R Paula09/2014
92492^177380-11304553397Enzo Doria07/2014
92505^76362-2*3^7636253375Mike Oakes11/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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